This study proposes a novel modeling approach based on an Adaptive Lightweight Trust-Region Reflective (AL-TRF) method for estimating all nine three-diode model (TDM) parameters under arbitrary irradiance and temperature conditions using only manufacturer datasheet information. The proposed AL-TRF scheme simultaneously identifies all nine model parameters under varying operating conditions. Its performance is validated using three PV modules representing multi-crystalline (SM55), mono-crystalline (ST40), and thin-film (S75) technologies. The results demonstrate accurate reproduction of prescribed datasheet characteristics and measured current–voltage (I–V) characteristics over a wide range of irradiance and temperature conditions. Compared with STC-only parameter transport, condition-wise identification reduces the pooled RMSE by 4.02%, 8.43%, and 26.68% for ST40, SM55, and S75, respectively. For the SM55 and S75 modules, AL-TRF achieves lower mean-condition RMSE than Harris Hawks Optimization (HHO) and Sunflower Optimization (SFO), with reductions of 1.75% and 18.76% relative to HHO and 66.24% and 24.13% relative to SFO, respectively. For ST40, despite slightly lower prediction errors obtained by the reference methods, AL-TRF retains a distinct modeling advantage through complete condition-wise identification of all nine TDM parameters. This comprehensive capability is achieved with substantially lower computational effort. In the single-STC SM55 benchmark, AL-TRF reduces execution time by 79.31% and 83.90% relative to HHO and SFO, respectively. For the complete modeling protocols, the corresponding reductions are 67.15% and 79.32% for ST40 and 82.12% and 82.12% for S75. Overall, AL-TRF provides a superior balance of predictive accuracy, complete condition-wise nine-parameter identification, and computational efficiency, establishing it as an effective datasheet-driven approach for reliable TDM reconstruction under widely varying operating conditions.